A semi-numerical method for periodic orbits in a bisymmetrical potential

We use a semi-numerical method to find the position and period of periodic orbits in a bisymmetrical potential, made up of a two dimensional harmonic oscillator, with an additional term of a Plummer potential, in a number of resonant cases. The results are compared with the outcomes obtained by the numerical integration of the equations of motion and the agreement is good. This indicates that the semi-numerical method gives general and reliable results. Comparison with other methods of locating periodic orbits is also made.Comment: Published in Mechanics Research Communication journal, 6 pages, 5 figures and 6 table

Revealing the influence of dark matter on the nature of motion and the families of orbits in axisymmetric galaxy models

An axially symmetric galactic gravitational model composed of a dense, massive and spherical nucleus with an additional dark matter halo component was used, to distinguish between the regular and chaotic character of orbits of stars that move in the meridional plane (R,z). We investigated two different cases: (i) a flat-disk galaxy (ii) an elliptical galaxy. It is of particular interest to reveal how the portion of the dark matter inside the main body of the galaxy influences the ordered or chaotic nature of motion. Varying the ratio of dark matter to stellar mass, we monitored the evolution not only of the percentage of chaotic orbits, but also of the percentages of orbits that compose the main regular resonant families, by classifying regular orbits into different families. Moreover we tried, to reveal how the starting position of the parent periodic orbits of each regular family changes with respect to the fractional portion of dark matter. We compared our results with previous similar work.Comment: Published in Astronomy & Astrophysics (A&A) journal. arXiv admin note: previous paper with related context: arXiv:1309.560